Codimension-1 subgroups and splittings of groups

DOI10.1006/jabr.1996.6884zbMath0873.20028OpenAlexW2042763636MaRDI QIDQ1355590

Michah Sageev

Publication date: 26 June 1997

Published in: Journal of Algebra (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1006/jabr.1996.6884

zbMATH Keywords

word hyperbolic groupsfinitely generated groupsCayley graphsnumbers of endsquasi-convex subgroupscodimension-1 subgroupssplitting amalgams

Mathematics Subject Classification ID

Subgroup theorems; subgroup growth (20E07) Geometric group theory (20F65) Free products of groups, free products with amalgamation, Higman-Neumann-Neumann extensions, and generalizations (20E06)

Related Items (29)

Cubulating rhombus groups. ⋮ A topological splitting theorem for Poincaré duality groups and high-dimensional manifolds ⋮ A generalized axis theorem for cube complexes ⋮ No quasi-isometric rigidity for proper actions on CAT(0) cube complexes ⋮ Hyperbolic groups acting improperly ⋮ Coarse injectivity, hierarchical hyperbolicity and semihyperbolicity ⋮ Projection complexes and quasimedian maps ⋮ VH-ification ⋮ Relative ends, \(\ell^2\)-invariants and property (T). ⋮ On embeddings of CAT(0) cube complexes into products of trees via colouring their hyperplanes ⋮ Thurston's vision and the virtual fibering theorem for 3-manifolds ⋮ Cubulating one-relator groups with torsion ⋮ Finiteness properties of cubulated groups ⋮ On strongly quasiconvex subgroups ⋮ Recubulating free groups. ⋮ Cubulating malnormal amalgams. ⋮ The singularity obstruction for group splittings ⋮ Property \(A\) and \(\text{CAT}(0)\) cube complexes. ⋮ Thurston’s Theory of 3-Manifolds ⋮ Packing subgroups in relatively hyperbolic groups. ⋮ Relative cubulations and groups with a 2-sphere boundary ⋮ Intersection properties of stable subgroups and bounded cohomology ⋮ Cubulating random groups at density less than $1/6$ ⋮ Splittings of groups and intersection numbers ⋮ Cross ratios and cubulations of hyperbolic groups ⋮ Geometric group theory and 3-manifolds hand in hand: the fulfillment of Thurston’s vision ⋮ Decomposing groups by codimension-1 subgroups ⋮ Cocompactly cubulated graph manifolds ⋮ On automorphisms and splittings of special groups

Cites Work

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• Relative ends and duality groups
• Ends of pairs of groups
• Groups acting on cubes and Kazhdan’s property (T)
• Ends of Group Pairs and Non-Positively Curved Cube Complexes
• An algebraic annulus theorem

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